Von Neumann Betti numbers and Novikov type inequalities

Details Von Neumann Betti numbers and Novikov type inequalities Von Neumann Betti numbers and Novikov type inequalities

1998-10-18

arxiv.org/abs/math/9810114v1

Mathematics

Differential Geometry

9 pages

Scientific paper

It is shown that the Novikov inequalities for critical points of closed
1-forms hold with the von Neumann Betti numbers replacing the Novikov numbers.
As a corollary we obtain a vanishing theorem for $L^2$ cohomology, generalizing
a theorem of W. Lueck. We also prove that von Neumann Betti numbers coincide
with the Novikov numbers for free abelian coverings.

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